Posamentier: Abandoning traditional math approach doesn’t add up

Wednesday, June 11, 2008BY ALFRED POSAMENTIERThe approach taken by the reformists is a nice form of enrichment, but it does not replace the need to teach children basic arithmetic skills.

FOR THE PAST FEW YEARS, parents and educators in this country seemed to be obsessed with the conflict about the best way to teach mathematics – particularly in the elementary grades.

This conflict, known nationally as “the math wars,” has recently flared up again in Wayne and Ridgewood, where the school system has been using a “reform program,” one that stresses arithmetic-concept understanding over algorithm skills.

The educational ideas that form the basis for this approach to teaching elementary mathematics are good and have their place on the instructional stage. Most math-savvy adults would agree that children should be exposed to these ideas, largely because they give students some useful quantitative insights.

However, when we adults look at this approach, we do so with a well-established arsenal of arithmetic skills; that is, we are thoroughly familiar with algorithms for the basic arithmetic operations, and we have many “number facts” solidly memorized.

Surely, from this vantage point, the approach taken by the reformists is a nice form of enrichment. But it does not replace the need to teach children basic arithmetic skills.

It is incumbent upon towns such as Wayne and Ridgewood to look at mathematics education from the vantage point of the learner who must get facility with arithmetic tools before, or while, being exposed to discovering quantitative patterns.

Familiarity with numbers

For example, if asked to multiply 25 x 28, some adults would say that this is equivalent to (25 x 4) x 7 = 100 x 7 = 700, or they might say 25 x 28 = (25 x 30) – (25 x 2) = 750 – 50 = 700, or other such combinations. However, we already know how to use an algorithm to multiply 28 x 25 directly. This sort of number facility might be less useful when multiplying 63 x 27, where the algorithm would be more desirable.

There is a school of thought among reformers that with today’s technology, arithmetic skills are less important. Yet, this position is taken by those who take their own arithmetic skills for granted.

As students gradually increase their quantitative talents – something we always enhance throughout our lives – they rely increasingly on the calculator, discounting their reliance on their now-well-ingrained arithmetic skill. They look at nifty number patterns and relationships and marvel at alternative ways of doing simple calculations based on these relationships.

Educators who discount their own arithmetic facility in making recommendations to others run the risk of providing inappropriate suggestions.

We constantly denigrate our own educational system – particularly when it comes to learning mathematics. We look overseas to other countries that seem to show better results on standardized testing. All too often, these tests are run on different types of populations and under different circumstances in different cultures, all of which clearly affect the outcome and render it inappropriate as a comparison.

Interestingly, many of these countries to whom we draw comparisons look to the United States as the educational paradigm to follow. This history of mathematics education of the past 50 years has been one of alternating fads, where we tend to go from one extreme to another, each time retaining some small particles from each extreme.

Aiming for the middle ground

We are once again at a point where the middle ground should be the goal.

Students must master arithmetic algorithms and as many number facts as they can, and then investigate number relationships and patterns, many of which they should be guided to discover on their own for a more genuine understanding.

The towns of Wayne and Ridgewood, which seem to have brought this issue to the surface through parental discontent, could serve to model these alternative forms of arithmetic calculation as mathematical enrichment, but only after students have attained a solid command of arithmetic, even if that is a somewhat traditional approach.

There is nothing wrong with a somewhat traditional approach. Quite the contrary, it is surely time-tested.

Alfred Posamentier of River Vale is dean of the School of Education at City College of New York and co-author of “Progress in Mathematics.”

“…Ridgewood … could serve to model these alternative forms of arithmetic calculation as mathematical enrichment, but only after students have attained a solid command of arithmetic…”

Don’t be fooled – This is not the ‘blended approach’ espoused by our BOE. Instead, Ridgewood’s version is backwards: The core curricula are Everyday Math or TERC, neither of which value nor teach a solid command of arithmetic. That’s left for enrichment. The real result is a mushy command of arithmetic, and ‘number sense’ that is of little use.

Our BOE should partner with Posamentier and City College, since our curriculum head seems to have difficulty with the overwhelming evidence against reform math that is just a few clicks away.

I’m still trying to understand why math curricula such as TERC and Everyday Math landed in Ridgewood. These NSF-spawned curricula were created to help educationally disadvantaged students. Now Ridgewood kids in elementary schools that have these programs are educationally disadvantaged too …. unless parents intervene. Nice job!

It just amazes me that people want to use our kids education as a platform for their own political axe-grinding. Someone on this blog even claimed that our schools have a socialist agenda! Give me a break — leave your political baggage at the door!!

sorry 622 public education is all politics nothing else , but heres soemthing for you to chew on the teachers union suports all these low livces that get elected in new jersey ,yet the state has stolen billions from the teachers pension plan ,what gives to many love letters to corzine?

What 6:22 fails to realize is that a new generation of adults, Generation X, have children in grade school.

They are not the hippies of the baby boom generation that invented and embrace this socialist constructivist math and science.

They grew up with Ronald Reagan not George McGovern as their role model.

They refuse to be patronized by a pot smoking generation that thinks everyone should feel good about themselves even if truth is a casualty.

Ergo, we have this conflict over math and the way it is taught. And since it is their kids who are being subjected to this dumb dumb math by the old guard establishment (baby boomers, who by the way didn’t inflict this crappy math on their kids) they are pissed and not going to stand for it.

So, here we are, one generation in charge, liberal by its place in history, facing off against another, younger, generation much more conservative by its place in history.

Funny, I bet the 60’s generation now in power never imagined that they would be the called “the establishment.” But there you have it. They are indeed. And now they are facing a challenge to their authority by a younger generation, Generation X, who aren’t buying into the peace, love and happiness routine when it comes to the education of their children.

8:06 the answer is simple. When a paper covers an issue, that issue lives in its archives. Whenever it comes up again as it did in Wayne, reporters have access to prior reporting by the paper and so tend to refer to previous stories in new stories. The math wars have not ended and references to Ridgewood, etc. will live on. In northern NJ, we are Ground Zero. Regina will be remembered as the architect of this carnage and Brennan the enabler.

It’s so stupid that we have a math war here in Ridgewood. That some people could actually fight to have weak math programs that adhere to low state standards is nothing short of evil. It can’t be dumb because no one is that dumb.

It occurred to me that if the Ridgewood district has it’s ‘A’ game going in math instruction, in terms of looking out for the best interests of each of its math students, it would have ensured that at least one Ridgewood Public Schools representative attended the math-related event referred to in the press release. Does anyone know whether or not one did?

William H. Sadlier, Inc., publisher of K12 instructional programs in mathematics and reading/language arts, announced today that the fifth annual meeting of the companys National Mathematics Advisory Board will be held on June 5, 2008, at the Newark (NJ) Airport Marriott Hotel.

The meeting brings together leading university-level researchers and scholars, public and private school administrators, and the companys mathematics authors, including Alfred S. Posamentier, PH.D., Dean, City College of New York, Catherine LeTourneau, Mathematics Department Chairperson, St. Catharine of Siena School, Reading, PA, and Edward William Quinn, Director of Elementary Curriculum, Instruction, and Staff Development for the Archdiocese of PA, for a day-long discussion of topics of interest to the K12 educational community.

Highlighting this years meeting will be reports and first-hand observations from two Board members who also served as members of the National Mathematics Advisory Panel (NMP) appointed in 2006 by President George W. Bush. Sandra Stotsky, Ph.D., Professor of Education Reform, 21st Century Chair in Teacher Quality, University of Arkansas, and Chair of the National Mathematics Advisory Board; and Vern Williams, Mathematics Department, Longfellow Middle School, Fairfax County, VA, will discuss the National Mathematics Advisory Panels recent recommendations concerning teacher training and the teaching of Algebra in todays schools.

Other highlights of the June 5 meeting include an update on the research study being conducted by Board member David Klahr, Ph.D., Professor of Psychology, Carnegie Mellon University, From the Lab to the Classroom Teacher to an Automated Tutor: A Long Journey with a Small Package; a discussion of the introduction of Response to Intervention (RTI) in a large suburban NJ district, by Cheryl Dyer, Assistant Superintendent, Bridgewater-Raritan School District; and an interactive live demonstration of new whiteboard technology applications being used in middle schools today.